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  <title>Spherical Damper</title>
                                         
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<div align="center"> <img src="SphericalDamper.GIF" alt="Title"
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<div align="left"><b><u>Simulation Control</u></b><br>
     <b>time step</b>:         Time step for the numerical integration routine<br>
     <b>time</b>:                Duration of the simulation periond in seconds<br>
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   <b><u>Description</u></b><br>
   A damper in a rigid spacecraft in a circular orbit may be able to stabilize 
 the spacecraft <br>
   that otherwise goes unstable without it. To simulate such a behavior,
a  rigid spacecraft <br>
   with a damper of spherical shape was modeled as illustrated.<br>
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   <img src="DamperAndSpacecraft.GIF"
 alt="Illustration of a damper and spacecraft" width="541" height="364">
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       <b><u>Inputs</u></b><br>
   <b>Ixx</b>, <b>Iyy, Izz</b>                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160; &#160; Principal moments 
of inertia<br>
   <b>c &#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;</b>                              &#160; &#160; &#160; Damping 
Coefficient<br>
     <b>j </b>                              &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160; 
&#160; Spherical damper inertia<br>
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   <b><u>Initial Condition</u></b><br>
         <b>w1</b>, <b>w2, w3</b>:                  &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160; Spacecraft 
angular velocities  <br>
      <b>q1, q2, q3, q4</b>:             &#160;&#160;&#160; &#160;&#160; &#160;&#160;&#160; &#160; Quaternions<br>
      <b>alpha, beta, gamma</b>:    &#160;&#160;&#160; Damper angular velocities<br>
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